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## Grade 6 Supporting Idea 6: Data Analysis

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**Grade 6 Supporting Idea: Data Analysis**• MA.6.S.6.1 Determine the measures of central tendency (mean, median, and mode) and variability (range) for a given set of data. • MA.6.S.6.2 Select and analyze the measures of central tendency or variability to represent, describe, analyze and/or summarize a data set for the purposes of answering questions appropriately.**FAIR GAME: Prerequisite Knowledge**• MA.3.S.7.1: Construct and analyze frequency tables, bar graphs, pictographs, and line plots from data, including data collected through observations, surveys, and experiments. • MA.5.S.7.1: Construct and analyze line graphs and double bar graphs.**Skills Trace**• Add whole numbers, fractions, and decimals • Divide whole numbers, fractions, and decimals • Compare and order whole numbers, fractions, and decimals • Add whole numbers, fractions, and decimals • Divide whole numbers, fractions, and decimals • Compare whole numbers, fractions, and decimals • Subtract whole numbers, fractions, and decimals**Measures of Center**mean median mode**Model: finding the median**Find the median of 2, 3, 4, 2, 6, 5. Usea strip of grid paper that has exactly as many boxes as data values. Place each ordered data value into a box. Fold the strip in half. The median is at the fold.**Model: finding the mean**• Arrange interlocking/Unifix cubes together in lengths of 3, 6, 6, and 9. • Describe how you can use the cubes to find the mean, mode, and median. • Suppose you introduce another length of 10 cubes. Is there any change in i) the mean, ii) the median, iii) the mode?**Thinking about measures of center**The median of five numbers is 15. The mode is 6. The mean is 12. What are the five numbers? 6 n n 6 15**Thinking about measures of center**The median of five numbers is 15. The mode is 6. The mean is 12. What are the five numbers? 6 n n 6 15**Thinking about measures of center**The median of five numbers is 15. The mode is 6. The mean is 12. What are the five numbers? 6 a b 6 15**Thinking about measures of center**The median of five numbers is 15. The mode is 6. The mean is 12. What are the five numbers? 6 a b 6 15**Missing Observations: Mean**Here are Jane’s scores on her first 4 math tests: • 82 75 79 What score will she need to earn on the fifth test for her test average (mean) to be an 80%? A x N = T Jane has 316 points. She needs 400 points. How many more does she need? 84 points**Missing Observations: Mean**Here are Jane’s scores on her first 4 math tests: • 82 75 79 What score will she need to earn on the fifth test for her test average (mean) to be an 80%?**Missing Observations: Mean**Here are Jane’s scores on her first 4 math tests: • 82 75 79 There is one more test. Is there any way Jane can earn an A in this class? (Note: An “A” is 90% or above) What measure of center are we asking students to consider?**Missing Observations: Mean**Here are Jane’s scores on her first 4 math tests: • 82 75 79 There is one more test. Is there any way Jane can earn an A in this class? (An “A” is 90% or above)**Missing Observations: Median**Here are Jane’s scores on her first 4 math tests: • 82 75 79 What score will she need to earn on the fifth test for the median of her scores to be an 80%? • 79 80 82**Missing Observations: Median**What score will she need to earn on the fifth test for the median of her scores to be an 80%? • 79 80 82 70? 75? 79? 80? 81? 82? 83? 84? **Think, Pair, Share**• Construct a collection of numbers that has the following properties. If this is not possible, explain why not. mean = 6 median = 4 mode = 4 What is the fewest number of observations needed to accomplish this?**Think, Pair, Share**• Construct a collection of numbers that has the following properties. If this is not possible, explain why not. mean = 6 median = 6 mode = 4 What is the fewest number of observations needed to accomplish this?**Think, Pair, Share**• Construct a collection of 5 counting numbers that has the following properties. If this is not possible, explain why not. mean = 5 median = 5 mode = 10 What is the fewest number of observations needed to accomplish this?**Think, Pair, Share**• Construct a collection of 5 real numbers that has the following properties. If this is not possible, explain why not. mean = 5 median = 5 mode = 10 What is the fewest number of observations needed to accomplish this?**Think, Pair, Share**• Construct a collection of 4 numbers that has the following properties. If this is not possible, explain why not. mean = 6, mean > mode**Think, Pair, Share**• Construct a collection of 5 numbers that has the following properties. If this is not possible, explain why not. mean = 6, mean > mode**Adding a constant k**• Suppose a constant k is added to each value in a data set. How will this affect the measures of center and spread? 5 6 7 9 2 4 1 6 mean = 5 median = 5.5 mode = 6 range = 8**Adding a constant k**5 6 7 9 2 4 1 6 5+2= 6+2= 7+2= 9+2= 2+2= 4+2= 1+2= 6+2= 7 8 9 11 4 6 3 8 mean = 5 median = 5.5 mode = 6 range = 8 mean = 7 median = 7.5 mode = 8 range = 8**Multiplying by a constant k**• Suppose a constant k is multiplied by each value in a data set. How will this affect the measures of center and spread? 5 6 7 9 2 4 1 6 mean = 5 median = 5.5 mode = 6 range = 8